Symmetry of Infinitesimal (linear) strain tensor
Why do we have the infinitesimal (linear) strain tensor to be symmetric? The reasons, which I have understood so far are:
1. It is defined to be symmetric so that it behaves like a tensor.
2. The stress tensor, which is its energy conjugate, is symmetric, and hence the skew-symmetric part has no contribution towards strain energy.
Can anyone suggest more fundamental reason(s) for the symmetry of linear strain tensor, like the moment equlibrium leading to symmetry of the Cauchy stress tensor?
Thanks in advance,
Jayadeep U. B.